Ghost-penalty stabilization can also be combined with the concept of aggregation to design weakly aggregated schemes, as proposed in [1]}, [2]}. In these schemes, one makes use of the standard finite element space \(V_h\)  on the active mesh, and instead of strongly imposing constraints via an extension operator of interior degrees of freedom, the difference between \(V_h\)  and \(V_h^{\textrm {ag}}\)  is weakly penalized. Recall the discrete extension operator \(\mathcal {E}_{h}^{\mathrm {ag}}: V_{h}^{\mathrm {in}} \rightarrow V_{h}^{\mathrm {ag}} \in V_h\)  defined in Section REF  to define a mapping \(P^{\textrm {ag}}_h:V_h\ni v_h \mapsto \mathcal {E}_{h}^{\mathrm {ag}} (v_h|_{\mathcal {T}_h^{\textrm {in}}}) \in V_h^{\textrm {ag}}\) . The difference \(v_h - P^{\textrm {ag}}_hv_h\)  can then be penalized similarly as in (REF )
